Copyright 2016 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/MAE342.html

Communications! Space System Design, MAE 342, Princeton University!

Robert Stengel•! Antenna characteristics•! Power transmission and

reception•! Signals, information, and noise•! Analog and digital modulation•! Communication link budgets•! Laser communications

C bits/s( ) = BW log2SN

+1!"#

$%&

1

Typical Spacecraft Communications Architecture

2

Pisacane

High frequency signals Low frequency signals

Antenna Gain•! Isotropic (uniform) radiation of power, P, from the center of a sphere of radius, r•! Power per unit area (power density) of the sphere s surface

p = P 4!r2

•! Power received from isotropic radiator over area, S

PS = Sp

•! Power received over area, S, if all power is focused uniformly on that area by antenna with gain, G

PS = GSpS = P•! Power density in S with idealized focused antenna

pS = P GS•! Idealized antenna gain

G = PSpS

= 4!r2

S

! = beamwidth half-angle

3

Typical Antenna Pattern•! Gain vs. angle from boresight axis (2-D)•! Geff is average gain over beamwidth•! Beamwidth variously defined as –3 dB cone angle or half-angle

4

Pisacane

Communications Geometry•! Ground station communication and tracking limited

by its minimum elevation angle, !!•! Fixed (non-steerable) antenna must have sufficient

beamwidth to transmit or receive•! Antenna gains and radiated power must be

adequate, given slant range and noise environment

5

Pisacane

Beamwidth Coverage

•! Broad or narrow coverage may be desired

! (cone) " 21fd

, deg

f = carrier signal frequency, GHzd = reflector diameter, m

Beamwidth of reflector antenna

6Pisacane

One-Way Radio Communication Calculation Nomogram (GE, 1960)

7https://en.wikipedia.org/wiki/Nomogram

Relationship of Antenna Area and Signal Wavelength to Antenna Gain

Geff =4!Aeff

"2

Aeff = effective antenna area, m2

! = c / f = carrier signal wavelength, mc = speed of light " 3#108 m/sf = carrier signal frequency, Hz

Effective antenna gain (transmitting or receiving)

8

Relationship of Antenna Area and Signal Wavelength to Antenna Gain

Power received from the transmitter

Pr = prAr = GtPtAr

4!r2

pr = power density at receiving antennaAr = effective area of receiving antennaGt = gain of transmitting antenna

Pt = transmitted powerr = distance between transmitting antenna and receiving antenna

Power ratioPr (watts)Pt (watts)

= GtAr4!r2

9

Antenna Characteristics

10

Pisacane

Electric and Magnetic Fields of a Dipole Antenna

http://en.wikipedia.org/wiki/Antenna_(radio) 11

Linear and Circular Polarization of Waves

Transmit and receive antennas must be aligned for best communication

Left or right helical rotation of signal

12

Characteristics of Typical Spacecraft Antennas

Conical log spiral

antenna

Gain(dBi) = 10 log Antenna GainIsotropic Antenna Gain

13

Larson, Wertz

Alternative Expressions for Power Ratio

Pr (watts)Pt (watts)

= GtAr4!r2

= AtAr"r( )2

=

AtAr f2

cr( )2= GtGr"

2

4!r2= GrAt4!r2

Power ratio in decibels

10 log10PrPt

!"#

$%&(dB) =

Gt (dB)+10 log10 Ar (dB)'10 log10 4( (dB)' 20 log10 r(dB)14

Detected Power

PrPt(dB) = Pr

Pt

!"#

$%& ideal

(dB)' Absorption(dB)' Rainfall(dB)

±Multipath(dB)'CrossPolarization(dB)

Pr = Pcarrier + Pinformation ! PcarrierPd = Pr + Pn

•! Receiver s detected power, Pd, includes components from–! transmitter s carrier signal–! information signal–! noise

15

Noise Sources

Receiver thermal and front end noiseAtmospheric, cosmic, solar, and man-

made noise

Pn =Pnatmosphere + Pnsolar + Pncosmic + Pnman!made + Pnreceiver

16

Atmospheric Attenuation, Multipath, and Ionospheric Effects on Space-

Earth CommunicationPrPt

(dB) = PrPt

!"#

$%& ideal

(dB)' Absorption(dB) – Rainfall(dB)

± Multipath(dB) – CrossPolarization(dB)

17

Pisacane

Receiver Noise

18Pisacane

Other Noise SourcesPn !" n or 1 f n

Solar NoiseCosmic and

Atmospheric Noise

19Pisacane

Receiver Noise

Pn = kT BW (watts)

T = 290 10NF (dB)/10 !1( )= 290 F !1( )

k = Boltzmann's constant = 1.38 !10"23 W-s / KT = effective receiver temperature, K

BW = bandwidth, HzNF = receiver noise figureF = receiver noise factor

Power and temperature

Power density No = Pn / BW= kT (watts/Hz) 20

Typical Spacecraft System Noise Temperature

21

Signal-to-Noise Ratio and Information Content

SN

= Pr (watts)Pn (watts)

SNdB( ) = Pr dB( )! Pn dB( )

Pr dB( ) ! 10 log Pr (watts)1watt

"#$

%&'

Channel capacity

C bits/s( ) = BW log2S + NN

!"#

$%&

= BW log2SN

+1!"#

$%&

BW = bandwidth, Hz22

Signal-to-Noise Ratio per Bit, Eb/No

S = received signal powerN = received noise powerBW = bandwidth of receiver

R = data bit rate

Eb : energy per bitNo :noise power spectral density

Eb

No

= SNBWR

How would you express this in decibels?

23

Communication: Separating Analog Signals from Noise

SDR !

2"#$%

&'( = SDR f( ) = Signal Power Spectral Density f( )

Noise Power Spectral Density f( ) !PSDsignal f( )PSDnoise f( )

Signal-to-Noise Spectral Density Ratio, SDR(f)

H f( ) = PSDsignal f( )PSDsignal f( ) + PSDnoise f( ) =

SDR f( )SDR f( ) +1

Optimal (non-causal) Wiener Filter, H(f)

24

Communication: Bit Rate Capacity of a Noisy Channel

Shannon-Hartley Theorem, C bits/s

C = BW log2SN

+1!"#

$%& = BW log2 SNR +1( )

S = Signal Power, e.g., wattsN = Noise Power, e.g., wattsBW = Channel Bandwidth, HzC = Channel Capacity, bits/s

25

Information Bandwidthfc = carrier frequency, Hz

BW = !f = f2 " f1 = information signal bandwidth, Hz

•! Low-frequency information signal superimposed on (i.e., modulates) high-frequency carrier radio signal for transmission

•! Information signal formats–! Analog (continuous)–! Digital (discrete)–! Digitized analog (i.e., A/D

conversion)

Power spectral density of transmitted signal

26

Entropy Measures Information Content of a Signal

•! H = Entropy of a signal encoding I distinct events

H = ! Pr(i) log2 Pr(i)i=1

I

"

•! Entropy is a measure of the signal s uncertainty–! High entropy connotes high uncertainty–! Low entropy portrays high information

content•! i = Index identifying an event encoded by a signal •! Pr(i) = Probability of ith event•! log2Pr(i) = Number of bits required to characterize

the probability that the ith event occurs

0 ! Pr(.) ! 1log2 Pr(.) ≤ 00 ! H ! 1

27

Entropy of Two Events with Various Frequencies of Occurrence

•! Frequencies of occurrence estimate probabilities of each event (#1 and #2)

H = H #1 + H #2

= !Pr(#1) log2 Pr(#1)! Pr(#2) log2 Pr(#2)

•! –Pr(i) log2Pr(i) represents the channel capacity (i.e., average number of bits) required to portray the ith event

log2 Pr #1 or # 2( ) ≤ 0

Pr(#1) = n #1( )N

Pr(#2) = n #2( )N

= 1! n #1( )N

•! Combined entropy

28

Entropy of Two Events with Various Frequencies of Occurrence

Entropies for 128 TrialsPr(#1) - # of Bits(#1) Pr(#2) - # of Bits(#2) Entropy

n n/N log2(n/N) 1 - n/N log2(1 - n/N) H1 0.008 -7 0.992 -0.011 0.0662 0.016 -6 0.984 -0.023 0.1164 0.031 -5 0.969 -0.046 0.2018 0.063 -4 0.938 -0.093 0.33716 0.125 -3 0.875 -0.193 0.54432 0.25 -2 0.75 -0.415 0.81164 0.50 -1 0.50 -1 196 0.75 -0.415 0.25 -2 0.811112 0.875 -0.193 0.125 -3 0.544120 0.938 -0.093 0.063 -4 0.337124 0.969 -0.046 0.031 -5 0.201126 0.984 -0.023 0.016 -6 0.116127 0.992 -0.011 0.008 -7 0.066

Entropy of a fair coin flip = 129

Accurate Detection of Events Depends on Their Probability of Occurence

Signals Rounded to Their Intended Values

30

Accurate Detection of Events Depends on Their Probability of Occurrence

! noise = 0.1

! noise = 0.2

! noise = 0.4

31

Analog Amplitude, Frequency, and Phase Modulation of Carrier Signal

32Fortescue

Sampling and Digitization

33Fortescue

Digital Amplitude-, Frequency-, and Phase-Shift Modulation of Carrier Signal

34Fortescue

Digital vs. Analog Modulation

PCM: pulse-code modulationFM: frequency modulationAM: amplitude modulation

•! Analog–! Amplitude modulation

conserves bandwidth–! Frequency modulation

spreads information bandwidth over larger RF bandwidth

•! Digital–! Pulse-code modulation

(particularly phase-shift keying) uses RF power most efficiently

35Pisacane

Link Budget for a Digital Data Link

Eb

No

=

PtLlGtLsLaGr

kTsR

Pt = transmitter powerLl = transmitter-to-antenna line loss

Gt = transmit antenna gainLs = space loss

La = transmission path lossGr = receive antenna gaink = Boltzmann's constant

Ts = system noise temperature

Eb

No

= SNBWR

Link budget design goal is to achieve satisfactory Eb/No by choice of link parameters

… in decibels?

36

Bit Error Rate vs. Eb/No

•! Goal is to achieve lowest bit error rate (BER) with lowest Eb/No

•! Implementation losses increase required Eb/No

•! Link margin is the difference between the minimum and actual Eb/No

•! BER can be reduced by error-correcting codes–! Number of bits

transmitted is increased–! Additional check bits

allow errors to be detected and corrected

37Pisacane

Performance of Coding/Decoding Methods

38

Pisacane

Pe = Bit Error Rate (BER)BPSK = Binary phase-shift keying

Coding gain is net S/N improvement provided by adding check bits

Some Natural Numbering SystemsNatural numbers: non-negative, whole numbers

•! Other number systems–! Octal (Base 8)–! Hexadecimal

(Base 16)–! DNA (Base 4)

[ATCG]

Denary (Base 10) Binary (Base 2) Unary (Base 1)0 0 ?1 1 12 10 113 11 1114 100 11115 101 111116 110 1111117 111 11111118 1000 111111119 1001 111111111

10 1010 111111111111 1011 11111111111

Digits Binary Digits Marks"Bits" (John Tukey)

Two 5-finger hands True-False Chalk and a rockOne 10-finger hand Yes-No Abacus

Present-Absent "Chisenbop" 39

American Standard Code for Information Interchange (ASCII) Code

http://en.wikipedia.org/wiki/Ascii

Binary Oct Dec Hex Glyph100 0000 100 64 40 @100 0001 101 65 41 A100 0010 102 66 42 B100 0011 103 67 43 C100 0100 104 68 44 D100 0101 105 69 45 E100 0110 106 70 46 F100 0111 107 71 47 G100 1000 110 72 48 H100 1001 111 73 49 I100 1010 112 74 4A J100 1011 113 75 4B K100 1100 114 76 4C L100 1101 115 77 4D M100 1110 116 78 4E N100 1111 117 79 4F O

7 data bits plus parity bitWidely used in computers 94 printable characters

40

Manchester Code for Telecommunication

•! Each data bit has one transition and occupies the same amount of time

•! Self-clocking•! Widely used on Ethernet

http://en.wikipedia.org/wiki/Manchester_code 41

Error Detection and Correction•! Parity check (simple)

–! Transmitter•! n Data bits added up•! Parity bit added to make sum

even•! n+1 bits transmitted

–! Receiver•! Check to determine if word is

odd or even•! If odd, odd number of errors has

been detected (but not corrected)–! Column-wise parity check of m

words determines where bits are corrupted

•! Additional bits must be transmitted

•! Turbo code (complex): see

http://en.wikipedia.org/wiki/Turbo_code 42

43

Typical Command and Telemetry Characteristics

Larson, Wertz

Communications Carrier Frequencies

DSCS-3

44Larson, Wertz

Typical Communication Satellite Transponder

Characteristics

45Larson, Wertz

46

GOES Communication Sub-System

Free-Space Laser Communication

Lesh, JPL, 1999

•! Diffraction limit of electro-magnetic beam is proportional to !/d•! ! = Wavelength•! d = aperture (diameter) of beam source•! Radio frequency wavelengths: cm – m•! Optical wavelengths: "m•! Up to 106 less beam spread for optical

communication

47

Lesh, JPL, 1999 48

Optical Communication Advantage Compared to Ka-Band RF #

(One-Way Pluto example, same power input)dB Factor Comparison13 Data Rate Increase 4.9 kbs vs. 270 bps26 Smaller Spacecraft

Aperture10 cm vs. 2 m

4 Less Transmitted Power Required

1 W vs. 2.7 W

7 Lower Transmitter Efficiency

5% vs. 28%

2 Lower System Efficiencies

24% vs. 40%

3 Atmospheric Loss -10 Smaller Ground

Station10 m vs. 34 m Lesh, JPL, 1999

49

Good News/Bad News for Optical Communication #

Lesh, JPL, 1999

•! Good news•! Higher bit rates possible•! Optical beams are narrower•! Energy concentrated on receiver

•! Bad News•! Optical beams are narrower•! Narrow beams must pointed more precisely•! Must track intended receiver•! RF may be preferred for acquisition,

command, and tracking•! Effects of cloud cover

50

51

52

LADEE Lunar LaserCom Space Terminal

53

LADEE LaserCom Components

54

Deep Space Network•! Command and telemetry•! Radar tracking (range,

elevation, and azimuth)•! Radiated signal power

drops off as 1/r2

•! Reflected return signal power drops off as 1/r2

•! Skin track return signal power drops off as 1/r4

•! Beacon (or transponder) on cooperative target–! Receives radiated signal–! Re-transmits fresh signal

•! Known time delay•! Different frequency

–! Return signal power drops off as 1/r2

Goldstone 70-m Antenna

55

DSN 64-m Antenna

56

Deep Space Network Coverage

JPL Control Center

57

58

Tracking and Data Relay Satellites

59

Next Time:!Telemetry, Command, Data

Handling & Processing!

60

!!uupppplleemmeennttaall MMaa""rriiaall

61

Signal-to-Noise Ratio per Bit, Eb/No

S = received signal powerN = received noise powerBW = bandwidth of receiver

R = data bit rate

Eb : energy per bitNo :noise power spectral density

Eb

No

= SNBWR

62